Adaptive stabilization for normal nonlinear discrete-time uncertain systems

In this paper, we develop a direct adaptive control framework for adaptive stabilization of the MIMO nonlinear uncertain systems, which can be represented as discrete-time normal form with input-to-state zero dynamics. The framework is Lyapunov-based and guarantees partial stability of the closed-loop systems, such that the adaptation of the feedback gain can stabilize the closed-loop system without the knowledge of the system parameters. We propose two controller designs with respect to different Lyapunov functions. Our results show that one of the adaptive laws can be characterized by Kronecker calculus. Two numerical examples are given to demonstrate the efficacy of the proposed frameworks.